# Examples for 8th grade - page 83

- Square

Calculate the perimeter and the area of square with a diagonal length 30 cm. - Ladder

Ladder 10 meters long is staying against the wall so that its bottom edge is 6 meters away from the wall. What height reaches ladder? - Distilled water

Sea water contains 5% salt. How many distilled water should be pour to 40 kg of sea water so that the salt content is 2%. How many kilograms of 2% of sea water we get? - Outer contact of circles

Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S_{1}S_{2}S_{3}. - PC disks

Peter has 45 disks in three colors. One-fifth of the disks are blue, red are twice more than the white. How much is blue, red and white disks? - Rectangle

The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm. - Football match 4

In a football match with the Italy lost 3 goals with Germans. Totally fell 5 goals in the match. Determine the number of goals of Italy and Germany. - Scale of map

James travels one kilometer in 12 minutes. The route walked for half an hour measured on the map 5 cm. Calculate how many kilometers James walked for half an hour. Find the scale of the map. - Two trains

There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway - Rhombus

If we increase the rhombus side by 2.4 cm; its perimeter is 20 cm. How long was the side of the rhombus? - Testing

Students of high school have 10 points for each good solved task. The wrong answer is deducted by 5 points. After solving 20 tasks, student Michael had 80 points. How many tasks did he solve correctly and how many wrong? - Pyramid four sides

In a regular tetrahedral pyramid is a body height 38 cm and a wall height 42 cm. Calculate the surface area of the pyramid; the result round to square centimeters. - Four integers

Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two. - Pyramid

The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid. - Doubling

The message is spreading that each day has doubled the number of people who know about it. All know message for 20 days. How long known it eighth people? - Comparing salaries

Spouses compared salaries. Mrs. Janka found that a 20% higher salary than Mr Jaroslav. Together earned € 1,430. How much they earn each of them? - Desribed circle to rectangle

Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%). - Cows

Agricultural cooperative has increased the number of housed cows by 14% to 285 units. By how many cows increased agricultural cooperative the number of cows? - Wall diagonal

Calculate the length of wall diagonal of the cube whose surface is 384 cm square. - Candies

The price for 1 kg of more expensive candies is 125 CZK. The price for 1 kg of cheaper candy is 100 CZK. We mix two different mixtures of candy. A) The first mixture contains 2 kg more expensive and 0.5 kg cheaper candy. Calculate the price for 1 kg of t

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